The contract also includes a team option for the 2021 season, according to ESPN. The deal could reach a total value of $6 million if next season's option is picked up.
Iglesias, 30, became a free agent in December when the Reds didn't tender him. He recorded a .288 batting average and set career highs with 11 home runs and 59 RBIs in 2019, his lone season in Cincinnati.
Iglesias, a 2015 All-Star selection with the Detroit Tigers, has a career .273 batting average with 32 homers and 247 RBIs.
Freddy Galvis is expected to serve as the Reds' starting shortstop next season. Cincinnati picked up his $5.5 million option in November.
The Reds acquired Galvis in a trade with the Toronto Blue Jays last season. He set career highs with 23 home runs and 70 RBIs in the 2019 campaign.